Exploring Mandelbrot Fractals

On the left you see the Mandelbrot set.

To calculate the following formular is used:

zn+1 = zn2 + c

This means that we build element after element (zn+1) of a chain depending on the previous element (zn) by squaring the previous and adding a constant element c.

Now we run the formular mapping each pixel of the canvas to a value of c = x + yi.

Starting with z0 = 0 this chain may explode (|zn| > 2) for some values of c after some time n.

  • If it explodes the coordinate for c is colored depending on n
  • if not the point c is inside the mandelbrot-set and it is colored dark gray.

When clicking into the picture the value of c (the coordinate) is shown and the path of zn is drawn in black.

Control with Mouse:

  • Ctrl + Left mouse button hold -> Zoom-Area
  • Shift + Left mouse button hold -> Move-Area
  • Ctrl + Right mouse button click -> Reset Zoom

Mandelbrot Set


Julia set


If we take the same formular as above (zn+1 = zn2 + c) and instead of mapping each pixel of the canvas to a value of c we map it to the starting z0=x+yi we get a slightly different fractal (click into the mandelbrot picture for setting c):